Average Error: 0.0 → 0
Time: 815.0ms
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r161164 = x;
        double r161165 = y;
        double r161166 = r161164 * r161165;
        double r161167 = 2.0;
        double r161168 = r161166 / r161167;
        double r161169 = z;
        double r161170 = 8.0;
        double r161171 = r161169 / r161170;
        double r161172 = r161168 - r161171;
        return r161172;
}
↓
double f(double x, double y, double z) {
        double r161173 = x;
        double r161174 = 1.0;
        double r161175 = r161173 / r161174;
        double r161176 = y;
        double r161177 = 2.0;
        double r161178 = r161176 / r161177;
        double r161179 = z;
        double r161180 = 8.0;
        double r161181 = r161179 / r161180;
        double r161182 = -r161181;
        double r161183 = fma(r161175, r161178, r161182);
        return r161183;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}} - \frac{z}{8}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}} - \frac{z}{8}\]

  5. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)}\]

  6. Final simplification0

    \[\leadsto \mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))